Why does the behavior of snap seem "weird"?
I believe you need to use the 3D Cursor for this.

In few words, you need to position the origin of the object in the right place first, then position the 3D Cursor where you need the object "by it's origin" to snap to.


Select the breaker.
In Edit mode select the bottom faces of the breaker, or a central vertex/edges/faces.
Shift + S > Cursor to Selected, now you have the 3D cursor at the bottom of the breaker in the center.
Go to Object mode.
Ctrl+Shift+Alt+C > Origin to 3D Cursor, now you have the origin of the breaker in the bottom center.
Select the plane, in Object mode, Shift+S > Cursor to Selected, again this will position the 3D cursor in the center of the plane.
Select the breaker, Shift+S > Selection to Cursor, now you moved the object "breaker" with the new origin that you positioned in step "5" to the center of the plane.


Hope this helps.